1. Introduction

Space Division Multiplexing (SDM) is a potential technology for optical fiber communication systems to meet the demand of increasing internet traffic [1]. The fast emerging new technologies for the Internet of Things (IoT) [2] and the ongoing pandemic situation expect even higher exponential growth of internet users across the globe [3]. The existing single-mode fibers (SMFs), time-wavelength division multiplexing, and digital coherent techniques have already reached their maximum limit of 80 Tb/s [4] and cannot go beyond this due to the threshold of non-linear effect and Shannon limit of maximum data rate [5]. One solution to this problem is space division multiplexing. The SDM technique came to prominence in early $2010$ [6], when different modes can act as different channels, increasing the existing capacity limits to transmit the data. The motivation to adopt such a system is easy integration with wavelength division multiplexing, shared hardware, reduced energy consumption, improved efficiency, and joint digital signal processing (DSP) [7].

The various demonstrated SDM fiber designs are single-mode multicore fiber (SM-MCF), few-mode multicore fiber (FM-MCF) and coupled core multicore fiber (CC-MCF) [8]. The SM-MCF consists of multiple single-mode cores with one common cladding, whereas FM-MCF consists of multiple few-mode cores with one common cladding. To date, the maximum data rate achieved by SM-MCF ($22$ core - $1$ mode) is 2.15 Pb/s over a length of 31 km [9] and FM-MCF ($38$ core - $3$ mode) is 10.66 Pb/s over a length of 11.3 km [10]. It is clear that the FM-MCF fibers have more potential to scale the data transmission capability than SM-MCF thanks to their few-mode nature. However, FM-MCF suffers from mode coupling leading to high crosstalk. The crosstalk can be reduced by increasing the difference between the effective refractive index of different modes. However, a large difference between effective indices can increase the differential mode delay (DMD) or differential mode group delay (DMGD). Therefore, there is a trade-off between mode coupling and DMD/DMGD.

Recently, a lot of work has been done on FM SDM fibers which include step-index, multi-step, graded-index, and graded-index with trench fibers [11]. There are two approaches for FM SDM fiber designs: first is a weakly coupled approach (ensuring low mode coupling with minimum $\Delta n_{\text {eff}}$ greater than $0.5 \times 10^{-3}$ (preferably $0.1 \times 10^{-3}$) but a high DMD) [12,13], wherein different mode groups act as different channels, and MIMO-DSP is only used if required. The second is a strongly coupled approach (ensuring low DMD in ps/km but high crosstalk) [14] wherein different modes with polarization act as different channels and MIMO-DSP is used to separate those modes at the receiver. The WC approach is widely used in mode-group-division-multiplexing (MGDM) wherein crosstalk between modes is minimized by maximizing $\Delta n_{\text {eff}}$, thus each LP mode can separately be detected using simple $2\times 2$ (non-degenerate LP modes) or $4\times 4$ (degenerate LP modes) MIMO techniques [15]. This $2\times 2$ or $4\times 4$ MIMO detection in MGDM is regardless of the number of LP modes, and hence DSP receiver complexity, over large DMD, is compromised for $2$ or $4$ parallel channels respectively. On the contrary, the SC approach is widely used in mode-division-multiplexing (MDM) wherein crosstalk is high due to low refractive indices differences between modes. It minimizes the DMD between modes so that simultaneous detection of each mode is possible through $2N\times 2N$ ($2$ polarization $\times \;N$ being the total number of spatial modes) MIMO DSP at the receiver. This low DMD between modes ensures the DSP system is cost-effective [16]. Thus, the SDM technique increases the system capacity by more than a $2N$ fold factor compared to single-mode fiber-driven systems. In general, the weakly coupled (WC) approach has been realized with step-index fiber (SI-FMF), whereas the strongly coupled (SC) approach has been realized with graded-index multi-mode fiber (GI-MMF) [17]. To date, a $4$-LP-mode WC step-index (SI) FMF has been demonstrated with a minimum $\Delta n_{\text {eff}}$ of $0.8 \times 10^{-3}$ and maximum $|\text {DMD}|$ of $8.5$ ns/km [18]. Here, the core radius is 7.5 $\mathrm{\mu}\textrm{m}$ and $n_{\text {co}}-n_{\text {clad}}$ is $0.0097$. Further, a $4$-LP-mode air trench-assisted SC few-mode multicore fiber has been demonstrated with a maximum $|\text {DMD}|$ of 45 ps/km and minimum $\Delta n_\text {eff}$ of $\approx \;10^{-5}$ [19,20]. Here, the core radius is $11.45$ µm, junction thickness between the core and trench is $3.3$ µm, trench thickness is $3$ µm and $n_{\text {co}}-n_{\text {clad}}$ is $0.009$.

In this paper, we investigate the different parameters: profile parameter ($\alpha$), core diameter ($a$), and refractive index difference between core and cladding ($\Delta n$) of a graded-index fiber to optimize the trade-off between the crosstalk and DMD for $4$-LP-mode (i.e., $\text {LP}_{01}$, $\text {LP}_{11}$, $\text {LP}_{21}$ and $\text {LP}_{02}$) WC and SC GIF. This study shows that $\alpha =2$ is not the only optimized parameter for graded-index fiber as used in different previous studies. A combination of $\alpha$, $n_{\text {co}}-n_{\text {clad}}$, and core radius is very important for the optimized performance of the fiber. Further, we investigate the narrow air trench-assisted GI-FMF to reduce the DMD as well as bending losses.

2. Graded-Index FMFs

Figure 1 shows the refractive index profile of a graded-index few-mode fiber. The parameters of the GI-FMF are: core radius ($a$), core refractive index ($n_{\text {co}}$), cladding refractive index ($n_{\text {clad}}$), and profile parameter ($\alpha$). The variation of the refractive index profile (RIP) is defined as:

 

Fig. 1. Graded-Index Profile

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3. High-NA GI-FMF

For high-NA GI, $4$-LP-mode fiber, first, we choose a high refractive index difference between core and cladding i.e. $n_{\text {co}}$-$n_\text {clad} = 0.016$. Once the refractive indices are set, we choose the core radius, $a$, such that only $4$-LP-mode can propagate using Normalized frequency, $V = \frac {2 \pi a}{\lambda }\ast$NA, where NA $= \sqrt {n^{2}(r) - n_{\text {clad}}^{2}}$. One may note from (1) that the $V$ values differ from $\alpha$ parameter to get any $p$ number of modes. We calculate the effective indices, effective area, and bend losses of different modes for a wide range of fiber parameters such as $n_{\text {co}}$-$n_\text {clad}$ from $0.014$ to $0.018$, core radius, $a$ from $7$ to $9$ µm, and profile parameter, $\alpha$ from $1$ to $9$. Using calculated effective indices of the modes, we further calculate the DMD of different fiber designs using (2).

The calculated results are represented by three sets of Figures. The first set of Figures 2, 3, 4 shows the variation of $n_{\text {eff}}$, DMD, and $A_{\text {eff}}$ respectively as a function of $\alpha$, for different $n_{\text {co}}-n_{\text {clad}}$ (a) $0.014$, (b) $0.016$, and (c) $0.018$, while the core radius is 7 $\mathrm{\mu}\textrm{m}$. Similarly, the second set of Figs. 5, 6, 7, and the third set of Figs. 8, 9, 10 show the above-mentioned variations for other core radii, $a$, of 8 and 9 $\mathrm{\mu}\textrm{m}$ respectively.

 

Fig. 2. Variation of $n_{\text {eff}}$ as a function of $\alpha$ when core radius $a$ = 7 $\mathrm{\mu}\textrm{m}$

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Fig. 3. Variation of DMD as a function of $\alpha$ when core radius $a$ = 7 $\mathrm{\mu}\textrm{m}$

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Fig. 4. Variation of $A_\text {eff}$ as a function of $\alpha$ when core radius $a$ = 7 $\mathrm{\mu}\textrm{m}$

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Fig. 5. Variation of $n_{\text {eff}}$ as a function of $\alpha$ when core radius $a$ = 8 $\mathrm{\mu}\textrm{m}$

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Fig. 6. Variation of DMD as a function of $\alpha$ when core radius $a$ = 8 $\mathrm{\mu}\textrm{m}$

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Fig. 7. Variation of $A_\text {eff}$ as a function of $\alpha$ when core radius $a$= 8 $\mathrm{\mu}\textrm{m}$

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Fig. 8. Variation of $n_{\text {eff}}$ as a function of $\alpha$ when core radius $a$= 9 $\mathrm{\mu}\textrm{m}$

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Fig. 9. Variation of DMD as a function of $\alpha$ when core radius $a$=9 $\mathrm{\mu}\textrm{m}$

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Fig. 10. Variation of $A_{\text {eff}}$ as a function of $\alpha$ when core radius $a$= 9 $\mathrm{\mu}\textrm{m}$

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Figures 2, 3, and 4, show that the DMD is lowest for $\alpha =2$ to $4$. Initially, the $n_{\text {eff}}$ difference between the higher order modes increases with increasing $\alpha$ and then saturates as the fiber’s RIP becomes closer to a step-index fiber. It is interesting to note that the degeneracy between the $\text {LP}_{21}$ and $\text {LP}_{02}$ breaks for $\alpha > 2$. Therefore, the region between $\alpha =3$ to $4$ is a good choice for reasonable low DMD $(< 6$ns/km$)$ and high $n_\text {eff}$ difference $(>0.5 \times 10^{-3})$ between different modes. Additionally, Fig. 4 illustrates that the changes in the $\alpha$ parameter have varying effects on the effective area of different modes. Specifically, the effective area of the $\text {LP}_{01}$ mode increases as the refractive index profile transits from a triangular profile to a step-index profile. Conversely, the effective area of the $\text {LP}_{02}$ mode decreases as the $\text {LP}_{02}$ mode evolves from a poorly guided mode to a well-guided mode with an increasing $\alpha$ parameter. Moreover, the effective area of the $\text {LP}_{11}$ mode initially decreases from $\alpha = 1$ to $3$ as it transforms from a poorly guided mode to a well-guided mode. However, it subsequently increases as $\alpha$ increases from $3$ to $9$, corresponding to the refractive index profile changing from a parabolic profile to a step-index profile. Furthermore, the effective area of the $\text {LP}_{21}$ mode remains relatively constant across varying values of the alpha parameter. This is due to its inherent resistance to perturbations in the refractive index profile, particularly for the higher-order modes. The perturbations caused by varying $\alpha$ from $9$ to $1$ primarily impact the lower-order modes, such as $\text {LP}_{01}$ and $\text {LP}_{11}$ [21].

These observed variations in $n_{\text {neff}}$, DMD, and effective mode area of the $\text {LP}_{01}$ and $\text {LP}_{02}$ modes show that $\alpha =2$ is not always an optimum parameter. The above observation shows that for a core radius of 7 $\mathrm{\mu}\textrm{m}$, $n_{\text {co}}-n_{\text {clad}}$ from $0.014$ to $0.018$, and $\alpha =3$ to $4$ provides an optimum balance between the DMD and $n_{\text {eff}}$ differences. This shows that the $\alpha$ parameter can limit the number of modes, and break the degeneracy between $\text {LP}_{02}$ and $\text {LP}_{21}$ mode (via increasing $n_{\text {eff}}$ differences). Thereby, it reduces the mode coupling and the $|\text {DMD}|$ in high-NA GI-FMF.

Further, we increase the core radius, $a$ to $8$ µm, and analyze the second set of Figs. 5, 6, 7. Figure 5(c) shows that at a high $n_{\text {co}}-n_{\text {clad}}$ of $0.018$, $\text {LP}_{31}$ and $\text {LP}_{12}$ modes start propagating, which is expected, therefore we limit the optimum $n_{\text {co}}-n_{\text {clad}}$ range from $0.014$ to $0.016$, this range is still wide enough from a fabrication perspective. Figure 6 shows that DMD is lowest between $\alpha =2$ to $3$, though acceptable for $\alpha =3$ to $4$. Further, it can be concluded that the curves for the DMD are going up with increasing $n_{\text {co}}-n_{\text {clad}}$ in both cases (i.e. for core radius, $a$, 7 to 8 $\mathrm{\mu}\textrm{m}$) and shifting towards the left with an increasing core radius for the same $n_{\text {co}}-n_{\text {clad}}$. Hence, the generic statement $\alpha$ is equal to $2$ is optimized for low DMD is not true, this too depends on $n_{\text {co}}-n_{\text {clad}}$ and core radius. The minimum DMD can be obtained for an optimum combination of $n_{\text {co}}-n_{\text {clad}}$, core radius, $a$, and $\alpha$. The optimum range of the $\alpha$-parameter over which low DMD can be obtained seems to have an inverse relation with core radius, $a$, and $n_{\text {co}}-n_{\text {clad}}$.

Similarly, increasing the core radius, $a$ to $9$ µm, in the third set of Figs. 8, 9, 10, provides similar sets of conclusions. Figure 8(a) shows higher order modes start propagating (i.e. $\text {LP}_{31}$ and $\text {LP}_{12}$) at $\alpha =4$. However, at high $n_{\text {co}}-n_{\text {clad}}$ of $0.016$ and $0.018$, Figs. 8(b) and (c) show higher order modes start propagating at $\alpha =3$ and $2$ respectively. Hence, for the core radius of $9$ µm, we restrict the $\alpha$ parameter to $2$ and the $n_{\text {co}}-n_{\text {clad}}$ range from $0.014$ to $0.016$ to allow $4$-LP-mode. Here, the effective area is larger, which is expected with increasing core diameter. The results have been summarised in Table 1, which shows the optimum range of $\alpha$ for the best combination of low DMD and large $n_{\text {eff}}$ differences between modes, as a function of core radius, $a$, and high-NA, $n_{\text {co}}-n_{\text {clad}}$. It shows that core radii of 7 and 8 $\mathrm{\mu}\textrm{m}$ are suitable for high-NA GI-FMF, which provides large $n_\text {eff}$ differences between modes as well as low DMD but at the cost of lower effective area. Since this high-NA GI-FMF has large $|\Delta n_\text {eff}|$ ( $> 0.5 \times 10^{-3}$), can be named as weakly-coupled (WC) GI-FMF. The optimized parameters for this WC-GI-FMF are core radius, $a$=8 $\mathrm{\mu}\textrm{m}$, $n_{\text {co}}-n_{\text {clad}}=0.014$, and $\alpha = 4$, which shows a good balance between the large Min.$|\Delta n_{\text {eff}}|$ of $0.6 \times 10^{-3}$, and low Max.$|\text {DMD}|$= 5.42 ns/km with a reasonable $A_\text {eff}$ of $80$ µm² and bending loss of higher order mode is $0.005$ ($\ll 10$ dB/turn) at a $10$ mm bend radius.

Table 1. Characteristics of High-NA GI-FMF

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4. Low NA GI-FMF

Similarly, to realize a $4$-LP-mode, low-NA GI-FMF, we choose a low refractive index difference between core and cladding i.e. $n_{\text {co}}$-$n_\text {clad} = 0.005$. Once the refractive indices are set, we choose core radius, $a$ such that only $4$-LP-mode can propagate using Normalized frequency, $V = \frac {2 \pi a}{\lambda }\ast$NA, where NA $= \sqrt {n^{2}(r)-n_{\text {clad}}^{2}}$. Since NA is low i.e. $n_{\text {co}}$-$n_\text {clad}$ is low, the higher order modes ( $\text {LP}_{21}$ and $\text {LP}_{02}$) are less confined to the core and tend to have high bending losses. Hence, We calculated the effective indices, effective area, and bend losses of different modes for a wide range of fiber parameters such as $n_{\text {co}}$-$n_\text {clad}$ from $0.004$ to $0.006$, core radius, $a$ from 7 to 9, and profile parameter, $\alpha$ from 1 to 9. Using calculated effective indices of modes, we further calculated the DMD of different fibers design using (2).

The calculated results are represented by three sets of Figures. The first set of Figs. 11 and 12 shows variation of $n_{\text {eff}}$ and DMD respectively as a function of $\alpha$, for different $n_{\text {co}}-n_{\text {clad}}$ (a) $0.004$, (b) $0.005$, and (c) $0.006$, while the core radius is 12 $\mathrm{\mu}\textrm{m}$. Similarly, the second set of Figs. 13, 14, and the third set of Figs. 15, 16, show the above-mentioned variations for other core radii, $a$, of 13 and 14 $\mathrm{\mu}\textrm{m}$ respectively.

 

Fig. 11. Variation of $n_{\text {eff}}$ as a function of $\alpha$ when core radius $a$= 12 $\mathrm{\mu}\textrm{m}$

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Fig. 12. Variation of DMD as a function of $\alpha$ when core radius $a$= 12 $\mathrm{\mu}\textrm{m}$

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Fig. 13. Variation of $n_{\text {eff}}$ as a function of $\alpha$ when core radius $a$= 13 $\mathrm{\mu}\textrm{m}$

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Fig. 14. Variation of DMD as a function of $\alpha$ when core radius $a$= 13 $\mathrm{\mu}\textrm{m}$

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Fig. 15. Variation of $n_{\text {eff}}$ as a function of $\alpha$ when core radius $a$= 14 $\mathrm{\mu}\textrm{m}$

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Fig. 16. Variation of DMD as a function of $\alpha$ when core radius $a$= 14 $\mathrm{\mu}\textrm{m}$

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Figures 11, 13, and 15 show that the $n_{\text {eff}}$ maximum in low-NA GI-FMF is below $1.45$, whereas Figs. 2, 5, and 8 show that the $n_{\text {eff}}$ range in High-NA GI-FMF is up to $1.462$. This shows that the variation of $n_{\text {eff}}$ with respect to $\alpha$ in low-NA GI-FMF is slower as compared to high-NA GI-FMF. This concludes that the effective indices differences, $\Delta n_{\text {eff}}$, between fundamental and higher modes are lower ($< 10^{-4}$) in low-NA GIF. Therefore, the range of $|\text {DMD}|$ in Figs. 12, 14, and 16 is smaller (less than $6$ ns/km), compared to high-NA GI-FMF (less than $20$ ns/km). Moreover, the lowest DMD range shift towards lower $\alpha$ for increasing $n_{\text {co}}-n_{\text {clad}}$. The conclusion drawn in the previous section is also valid here: $\alpha$, over which low DMD can be obtained, seems to have an inverse relation with core radius, $a$, and $n_{\text {co}}-n_{\text {clad}}$. One may note that the effective area in low-NA GI-FMF is always larger than $100$ µm² for a range of the investigated parameters. However, the bending loss (BL) of the higher order modes is also higher due to low $n_{\text {co}}-n_{\text {clad}}$. The bending losses should be maintained below $10$ dB/turn at a $10$ mm bending radius [17]. Further, this (BL) can be controlled through trench-assisted GI-FMF [22]. The conclusions for low-NA GI-FMF have been summarised in Table 2, since low-NA GI-FMF provides lower DMD, we provide an optimum range of $\alpha$ for lower DMD while keeping the $|\Delta n_{\text {eff}}|$ as high as possible. The table includes lowest DMD within $\alpha$ range and their corresponding $|\Delta n_{\text {eff}}|$ between $\text {LP}_{02}$ and $\text {LP}_{21}$. The low-NA GI-FMF has $|\Delta n_{\text {eff}}|$ values lower than $0.5 \times 10^{-3}$. These very small effective indices differences lead to strong coupling between the modes, therefore named strongly-coupled (SC) GI-FMF. The optimized parameters for this SC-GI-FMF are core radius, $a$=14 $\mathrm{\mu}\textrm{m}$, $n_{\text {co}}-n_{\text {clad}}=0.005$ and $\alpha =3$, which shows the lowest $|\text {DMD}|$ of 0.9 ps/km with Min.$|\Delta n_{\text {eff}}|$ of $0.1 \times 10^{-3}$. The lowest DMD value can even be tuned further in $10$s of ps/km via tweaking $\alpha$ up to two decimal points. Therefore, the SC-GI-FMF are very sensitive to process variability. In this case, the bending losses are higher ($6$ dB/turn at $10$ mm bend radius) due to lower NA and can be compensated through air trench-assisted SC-GI-FMF. The achievement of this low-NA air trench-assisted fiber is sub-nanosecond DMD per kilometer.

Table 2. Characteristics of Low-NA GI-FMF

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5. Design of narrow air trench-assisted Low-NA GI-FMF

This section explores a narrow air trench around a low-NA GI-FMF for reducing bend loss. This type of fiber is known to have lower DMD and BL thanks to the air trench [23]. Figure 17 shows the schematic of the refractive index profile of narrow air trench-assisted GI-FMF. The parameters are core radius ($a$), refractive index difference between core and cladding ($\Delta n$), junction thickness between the trench and core ($r$), and trench thickness ($w$).

 

Fig. 17. Narrow Air tench-assisted Graded-Index Profile

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For a $4$-LP-mode fiber, $V$ is set at $7.5$ ($\alpha =2$, representing a strong coupling where both the modes $\text {LP}_{21}$ and $\text {LP}_{02}$ have almost the same $n_{\text {eff}}$). We choose the core radius, $a$ = 14 $\mathrm{\mu}\textrm{m}$ (to ensure low DMD as discovered in section 4). Once the radius is defined, we set $\Delta n$ ($n_{\text {co}}-n_{\text {clad}}$) $= 0.006$, calculated via $V = \frac {2 \pi a}{\lambda } \ast$NA where $\text {NA}=\sqrt {(n^{2}_{\text {co}}-n^{2}_{\text {clad}})}$. Figure 18(a), (b), and (c) shows the variation of DMD and $n_{\text {eff}}$ as a function of junction thickness ($r$), trench thickness ($w$), and profile parameter ($\alpha$) respectively. The DMD has been shown here between $\text {LP}_{01}$ and all the three modes i.e. $\text {LP}_{11}$, $\text {LP}_{21}$, $\text {LP}_{02}$. To reduce the DMD lower than 100 ps/km, the trench parameters $r$, $w$, and $\alpha$ play a very significant role as shown in Fig. 18. Moreover, the $n_{\text {eff}}$ of $4$-LP-mode air trench-assisted low-NA GIFs are insensitive to these changes, which means we can minimize the DMD by adjusting these trench parameters. For example, we can set $r$ from 4 $\mathrm{\mu}\textrm{m}$ to 4.5 $\mathrm{\mu}\textrm{m}$, $w$ from 0.1 $\mathrm{\mu}\textrm{m}$ to 0.2 $\mathrm{\mu}\textrm{m}$, and $\alpha$ from $1.97$ to $2.02$, to reduce the DMD lower than 50 ps/km. Table 3 summarizes the optimized parameters for narrow air trench-assisted low-NA GI-FMF for $4$-LP-mode. The lowest DMD achieved for narrow air trench-assisted low-NA GI-FMF is 16 ps/km, whereas it is $0.9$ ns/km without a trench (in section 4).

 

Fig. 18. Variation of DMD and $n_{\text {eff}}$ as a function of (a) $r$, (b) $w$ and (c) $\alpha$

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Table 3. Characteristics of narrow air trench GI-FMF when $a$=14 $\mathrm{\mu}\textrm{m}$, $r$ = 4 $\mathrm{\mu}\textrm{m}$, $w$=0.18 $\mathrm{\mu}\textrm{m}$ and $\alpha =1.98$

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6. Conclusion

We conclude that the range of profile parameter ($\alpha$) for GI-FMF (over which low DMD can be obtained) is inversely proportional to the core radius, $a$ and $n_{\text {co}}-n_{\text {clad}}$ in both high-NA and low-NA GI-FMF. The high-NA GI-FMF has weak coupling between modes i.e. large effective indices differences, hence termed WC-GI-FMF. Similarly, the low-NA GI-FMF has strong coupling between modes i.e. low effective indices differences, hence termed SC-GI-FMF. The optimized parameters for WC-GI-FMF are core radius, $a=8$ µm, $n_{\text {co}}-n_{\text {clad}}=0.014$, and $\alpha = 4$, which shows a large $\Delta n_{\text {eff}}$ of $0.6 \times 10^{-3}$ as well as low $|\text {DMD}|$ of 5.4 ns/km with a reasonable $A_{\text {eff}}$ of 80 $\mathrm{\mu}\textrm{m}^{2}$ and bending loss of higher order mode is $0.005$ dB/turn at a $10$ mm bend radius. Similarly, the optimized parameters for SC-GI-FMF are core radius, $a$=14 $\mathrm{\mu}\textrm{m}$, $n_{\text {co}}-n_{\text {clad}}=0.005$, and $\alpha = 3$, which shows minimum $\Delta n_{\text {eff}}$ of $0.1 \times 10^{-3}$ and the lowest $|\text {DMD}|$ of 0.9 ns/km while the maximum bending loss (BL) of the higher order mode is 6 dB/turn at a $10$ mm bend radius. The BL of SC-GI-FMF can be controlled through trench-assisted GI-FMF. The investigated narrow air trench GI-FMF has the lowest DMD of 16 ps/km, while the maximum BL of $\text {LP}_{02}$ mode is $0.45$ (much lower than $10$ dB/turn). Thus, one can opt for high-NA GI-FMF (WC-GI-FMF) offering lower mode coupling and non-degenerate $\text {LP}_{02}$ and $\text {LP}_{21}$ modes but at the cost of high DMD and low $A_{\text {eff}}$. On the other hand, one can opt for low-NA GI-FMF (SC-GI-FMF) offering lower DMD and higher effective area but at the cost of slightly higher mode coupling.